Bane - kapena madalitso
Ophunzira nthawi zambiri sakonda kuwerenga ndi ma logarithms. Mwamwayi, amadziwika kuti amathandizira kuchulutsa manambala powachepetsa mpaka ? ndikosavuta? kuwonjezera, koma mumazitenga mopepuka. Ndani akanasamala? lero, mu nthawi ya zowerengera zopezeka paliponse ngakhale m'mafoni a m'manja? mukuda nkhawa kuti kuchulukitsa mwaukadaulo ndikovuta kwambiri kuposa kuwonjezera: pambuyo pake, onse adatsikira kukanikiza makiyi angapo?
Zoona. Koma mpaka posachedwa? osachepera pa sikelo ya nthawi ya omwe asayina pansipa? zinali zosiyana kotheratu. Tiyeni titenge chitsanzo ndikuyesera kuchulukitsa osagwiritsa ntchito chowerengera? ena awiri akuluakulu; tiyeni tinene kuti tichitepo kanthu 23 × 456. Si ntchito yabwino kwambiri, sichoncho? Pakadali pano, mukamagwiritsa ntchito ma logarithms, chilichonse chimakhala chosavuta. Timalemba mawu olembedwa:
chipika (23 456 789 × 1 234 567) = chipika 23 456 789 + chipika 1 234 567 = 7,3703 + 6,0915 = 13,4618
(timadzipatula ku malo anayi a decimal, popeza izi nthawi zambiri zimakhala zolondola pamizere yosindikizidwa ya logarithmic), ndiye kuti logarithm ndi? zomwe timawerenganso kuchokera m'magome - pafupifupi 28. Pomaliza. Zotopetsa koma zosavuta; pokhapokha, ndithudi, muli ndi ma logarithms okhazikika.
Ndakhala ndikudzifunsa kuti ndani adabwera ndi lingaliro ili poyamba? ndipo ndinakhumudwa kwambiri pamene mphunzitsi wanga wa masamu wosaiŵalika wa sukulu Zofia Fedorovich adanena kuti sikunali kotheka kukhazikitsa kwathunthu. Mwina Mngelezi wina dzina lake John Napier, yemwe amadziwikanso kuti Napier. Kapena mwina mnzake wakale Henry Briggs? Kapena mwina mnzake wa Napier, Swiss Jost Burgi?
Sindikudziwa za Owerenga lemba ili, koma ndimakonda mwanjira ina ngati chopangidwa kapena chopezeka chili ndi wolemba m'modzi. Tsoka ilo, izi sizili choncho: nthawi zambiri anthu angapo amakhala ndi lingaliro lomwelo nthawi imodzi. Ena amatsutsa kuti njira yothetsera vuto kaŵirikaŵiri imawonekera ndendende pamene ikufunika malinga ndi zosowa za anthu, nthaŵi zambiri zachuma; zisanachitike, monga lamulo, palibe amene amaganiza za izo?
Ndiye nthawi inonso? ndipo izo zinali zaka khumi ndi zisanu ndi chimodzi, izo zinali. Kukula kwachitukuko kumakakamizika kuwongolera njira zamakompyuta; kusintha kwa mafakitale kunali kugogoda pazipata za Ulaya.
Ndendende pakati pa zaka za m'ma 1550? pa XNUMX? wobadwira ku Scotland, m'banja la Merchiston Castle pafupi ndi Edinburgh, Ambuye John Napier yemwe tatchulawa. Zikuoneka kuti njonda imeneyi ankaonedwa ngati munthu wachabechabe kuyambira ali wamng'ono: m'malo mwa moyo wamba ndi wosangalatsa wa olemekezeka, iye anachita chidwi ndi zopangidwa? komanso (zomwe zinali zosowa kale) masamu. Komanso? m'malo mwake, zinali zotani? alchemy? Anayesa kupeza njira yochotsera migodi ya malasha; adapanga makina ofananirako omwe masiku ano timawaganizira ngati akasinja kapena sitima yapamadzi; Anayesa kupanga magalasi omwe ankafuna kuwotcha zombo za Great Armada za Akatolika a ku Spain omwe ankaopseza Apulotesitanti ku England? Ankakondanso kukulitsa zokolola zaulimi pogwiritsa ntchito feteleza wopangira; mwachidule, Scot anali ndi mutu osati parade.
Komabe, palibe lingaliro lililonse lomwe likanamupatsa iye kusintha ku mbiri ya sayansi ndi luso lamakono, ngati si logarithms. Mfuti yake ya logarithmic idasindikizidwa mu 1614? ndipo nthawi yomweyo adadziwika ku Europe konse.
Nthawi imodzi ? ndi modziyimira pawokha, angakhale ena amalankhula pamaso pa mbuye wathu? Bwenzi lake lapamtima, Swiss Jost Burgi, nayenso anabwera ndi lingaliro la biluyi, koma ntchito ya Napier inadziwika. Akatswiri amanena kuti Napier anakonza ntchito yake bwino kwambiri ndipo analemba mokongola kwambiri, mokwanira. Choyamba, chinali chiphunzitso chake chomwe chinadziwika kwa Henry Briggs, yemwe, pamaziko a chiphunzitso cha Napier, adapanga matebulo oyambirira a logarithms ndi mawerengedwe otopetsa a pamanja; ndipo anali matebulo awa omwe pamapeto pake adakhala chinsinsi cha kutchuka kwa akauntiyo.
Monga mwanenera? chinsinsi cha computing logarithms ndi masanjidwe. John Napier mwiniyo sanali wokondwa kwambiri ndi mfundo iyi: kunyamula voliyumu yotupa ndikuyang'ana manambala oyenera mmenemo si njira yabwino kwambiri. N'zosadabwitsa kuti mbuye wanzeru (amene, mwa njira, sanakhale ndi malo apamwamba kwambiri mu utsogoleri wolemekezeka, wachiwiri kuchokera pansi m'gulu la olemekezeka a Chingerezi) anayamba kuganiza za kumanga chipangizo chanzeru kuposa magulu. Ndipo? adachita bwino, ndipo adalongosola mapangidwe ake m'buku lakuti "Rabdology", lofalitsidwa mu 1617 (izi, mwa njira, chinali chaka cha imfa ya wasayansi). Ndiye kodi timitengo tinapangidwa, kapena mafupa a Napier, chida chodziwika bwino cha makompyuta? pang'ono! ? pafupifupi zaka mazana awiri; ndi rhabdology palokha inali ndi zofalitsa zambiri ku Europe konse. Ndinawona makope angapo a mafupawa akugwiritsidwa ntchito zaka zingapo zapitazo ku Technological Museum ku London; zidapangidwa m'mitundu yambiri, zina mwazokongoletsa komanso zodula, ndinganene - zokongola.
Kodi ntchito?
Zosavuta. Napier adangolemba tebulo lodziwika bwino lochulutsa pamagulu a timitengo tapadera. Pa mlingo uliwonse? matabwa kapena, mwachitsanzo, opangidwa ndi fupa, kapena okwera mtengo kwambiri a minyanga ya njovu, yokongoletsedwa ndi golidi? Chogulitsa chochulukitsa chikachulukitsidwa ndi 1, 2, 3, ..., 9 chinali makamaka mwanzeru. Ndodozo zinali ndi makona anayi ndipo mbali zonse zinayi zinkagwiritsidwa ntchito kusunga malo. Chifukwa chake, gulu la ndodo khumi ndi ziwiri zidapatsa wogwiritsa ntchito ma seti 48. Ngati mumafuna kuchulutsa, mumafunikira kusankha kuchokera pamizere yolingana ndi manambala ochulukitsira, kuwayika moyandikana pachoyikapo, ndikuwerenga zinthu zina kuti muwonjezere pamodzi.
Kugwiritsa ntchito mafupa a Napier kunali kosavuta; pa nthawiyo zinali ngakhale zothandiza kwambiri. Komanso, amamasula wogwiritsa ntchito kuloweza tebulo lochulutsa. Anapangidwa m'matembenuzidwe ambiri; mwa njira, lingaliro losintha ndodo za quadrangular lidabadwa? yabwino kwambiri ndipo imanyamula zodzigudubuza zambiri.
Lingaliro la Napier? ndendende mu mtundu wa odzigudubuza - wopangidwa ndikuwongoleredwa ndi Wilhelm Schickard popanga makina ake owerengera, omwe amadziwika kuti "mawotchi owerengera".
Wilhelm Schickard (wobadwa April 22, 1592 ku Herrenberg, anamwalira pa October 23, 1635 ku Tübingen) - katswiri wa masamu wa ku Germany, wodziwa zilankhulo za Kum'maŵa ndi mlengi, pulofesa pa yunivesite ya Tübingen komanso mtsogoleri wachipembedzo wa Lutheran; mosiyana ndi Napier, iye sanali wolemekezeka, koma mwana wa kalipentala. Mu 1623? Chaka chimene wafilosofi wamkulu wa ku France ndipo pambuyo pake anatulukira makina opangira masamu a Blaise Pascal adatumidwa ndi katswiri wa zakuthambo Jan Kepler kuti amange imodzi mwa makompyuta oyambirira a dziko lapansi omwe amapanga kuwonjezera, kuchotsa, kuchulukitsa ndi kugawa magawo. , "wotchi" yomwe tatchulayi. Makina amatabwa ameneŵa anapsa mu 1624 pa Nkhondo ya Zaka Makumi Atatu, pafupifupi miyezi isanu ndi umodzi itatha; Kodi idamangidwanso mu 1960 ndi Baron Bruno von Freytag? Leringhof kutengera mafotokozedwe ndi zojambula zomwe zili m'makalata opezeka a Schickard kupita kwa Kepler. Makinawa anali ofanana pang'ono m'mapangidwe awo ndi lamulo la slide. Inalinso ndi magiya okuthandizani kuwerenga. Ndipotu, chinali chozizwitsa cha luso lamakono pa nthawi yake.
Ndi inu?Penyani? Pali chinsinsi ku Shikard. Funso limadzuka: nchiyani chomwe chinapangitsa mlengiyo, atawononga makinawo, osayesa kukonzanso ndikusiya kugwira ntchito paukadaulo wamakompyuta? Kodi nchifukwa ninji, ali ndi zaka 11, anachoka kufikira imfa yake kukauza aliyense za “wotchi yake”? Sananene?
Pali lingaliro lamphamvu kuti kuwonongeka kwa makina sikunangochitika mwangozi. Limodzi la zongopeka pankhaniyi ndi lakuti tchalitchi chinaona kukhala chisembwere kupanga makina oterowo (kumbukirani chiweruzo cha pambuyo pake, cha zaka 0 zokha, chimene Bwalo la Inquisition linapereka pa Galileo!) Ndi kuwononga “wotchiyo”? Shikard anapatsidwa chizindikiro champhamvu kuti asayese "kulowa m'malo mwa Mulungu" m'derali. Kuyesera kwina kuchotsa chinsinsi? m'lingaliro la amene wasayina m'munsimu, mothekera? Zili ndi chakuti wopanga makinawo molingana ndi mapulani a Schickard, Johann Pfister, wopanga mawotchi, adalangidwa ndi kuwonongedwa kwa ntchito ndi abwenzi ake m'sitolo, omwe sanafune kuchita chilichonse molingana ndi zofuna za anthu ena. mapulani, amene ankaona kuphwanya lamulo la gulu.
Chirichonse chimene icho chiri? galimoto inayiwalika mwachangu ndithu. Zaka zana limodzi pambuyo pa imfa ya Kepler wamkulu, zina mwa zolemba zake zinapezedwa ndi Mfumukazi Catherine II; Patapita zaka zingapo, iwo anakafika kumalo otchuka a Soviet astronomical observatory ku Pulkovo. Atavomereza kusonkhanitsa kumeneku kuchokera ku Germany, Dr. Franz Hammer anapeza makalata a Schickard kuno mu 1958; nthawi yomweyo, zojambula za Schickard zopangira Pfizer zidapezeka m'gulu lina la zolemba ku Stuttgart. Malingana ndi deta iyi, makope angapo a "wotchi" anamangidwanso. ; mmodzi wa iwo anatumidwa ndi IBM.
Mwa njira, Afalansa sanasangalale ndi nkhani yonseyi: mnzawo Blaise Pascal kwa zaka zambiri ankaonedwa kuti ndi mlengi wa njira yoyamba yowerengera bwino.
Ndipo izi ndi zomwe mlembi wa mawuwa amawona kuti ndizosangalatsa komanso zoseketsa m'mbiri ya sayansi ndi zamakono: kuti apa, nayenso, palibe chomwe chikuwoneka ngati chomwe mukuganiza?
